How can we distinguish the valuable hypotheses from the useless ones, those which are useful to physics from those which are merely an encumbrance and should be rejected? This is not a question which can be solved by referring to abstract rules. In order to answer it, we must study the use of hypotheses where it is perfect, and decide according to this example. To my mind, says Comte, the deeper study of the art of hypotheses in astronomy can alone establish the rules which are suitable to direct the use of this precious artifice in physics, and more so still in the remainder of natural philosophy.[138] Now of what use is it to astronomers? To anticipate the results of deduction or of induction, “by making a provisional supposition concerning some of the very notions which constitute the final object of the research.” It is a process of which the methods of approximation used by geometers originally suggested the general idea. They “supposed” that the circumference was the limit of the perimeters of inscribed and circumscribed polygons the number of whose sides went on increasing. In the same way, hypotheses provisionally fill up the “lacunæ” of our knowledge. An hypothesis should always be open to a positive verification, “whose degree of precision is in harmony with that of the corresponding phenomena.” For it only expresses beforehand what experience and reasoning might have made known immediately, if the circumstances of the problem had been more favourable. If, therefore, an hypothesis claimed to attain that which in its nature is inaccessible to observation and to reasoning, it would immediately become illegitimate and harmful. In a word, it must bear exclusively upon laws, and never upon causes or the modes of production of phenomena. In the physics of his own time Comte finds the two kinds of hypotheses, but he also finds more bad hypotheses than good ones. He especially protests against the ethers and the fluids to which the phenomena of heat, light, electricity and magnetism were attributed. These hypotheses, according to him, are destined to disappear from science. It is true that the physicists deny that they attribute an objective reality to their ethers and their fluids. They claim to need them absolutely in order to facilitate the conception and the combination of phenomena. However, in spite of themselves, they are drawn into speaking of their ethers as if they really existed. Moreover, do they not see that astronomy gets on very well without similar hypotheses? In order to conceive the phenomena it is enough to observe and analyse them attentively. And, as to combining them, that depends upon the knowledge which has been obtained of their positive relations.